# 5 - Reality of Abstractions Consider the ideas of reality real, abstractly real, computationally real (see [Interpretation of Simulations](Interpretation%20of%20Simulations.md)). Very tightly linked to [10 - The Nature of Mathematics](10%20-%20The%20Nature%20of%20Mathematics.md) ## Link * [10 - The Nature of Mathematics](10%20-%20The%20Nature%20of%20Mathematics.md) * [Computation is the Window to the Abstract](Computation%20is%20the%20Window%20to%20the%20Abstract.md) * [Computations and Physical Processes Represent Abstract Concepts](Computations%20and%20Physical%20Processes%20Represent%20Abstract%20Concepts.md) * ## Seeking Good Explanations Forces us to Conclude Abstractions are Real ### Primality Testing Consider of the example [The Domino That Didn't Fall](The%20Domino%20That%20Didn't%20Fall.md). ### Taking 'Abstractions Are Not Real' Seriously But wait, when we were just [Forced To Take a Position](Forced%20To%20Take%20a%20Position.md) did we actually have two choices? Let's examine this a bit more closely. On the one hand we could claim that abstractions are real. On the other hand we could claim that abstractions are *non-real* but interact with *real* entities via some previously unknown mechanism. On the face of it that already appears to present a [Contradiction](Contradiction.md)! By definition, real entities are those that actually exist, and non-real entities do *not* exist. So logically it seems there is no way to create a coherent [Explanation](Explanations.md) that accounts for the interaction of non-real entities with real ones. The minute you start talking about non-real entities interacting with real ones, those non-real entities must be real in some way. But if we were arguing with [Mr Witt](Mr%20Witt.md) about this he may try and slip out of this contradiction with a [Renaming Scheme](Renaming%20Scheme.md). He may say "No no no, there are real and non-real entities. The non-real entities interact with real entities [As If](As%20If.md) they were real, but they are non-real. We can call them pseudo-real or semi-real if you'd like, in order to get around this apparent contradiction based on your provided definitions". Do you see what [Mr Witt](Mr%20Witt.md) did there? He used nearly the same argument as the [professor who was trying to defend solipsism](Defend%20Science%20by%20Arguing%20Against%20Arbitrary%20Boundaries.md#Argue%20Against%20Solipsism%20Take%20it%20Seriously). We can respond in turn by [Taking Mr Witt's Theory Seriously on It's Own Terms](Take%20Theories%20Seriously%20on%20Their%20Own%20Terms.md). All he has done is taken our idea that both abstract and physical entities are both real, and complicated it with his inexplicable [Renaming Scheme](Renaming%20Scheme.md)[^1]. But he ends up arguing for exactly what we are arguing for - bar the renaming scheme. Thus he has just complicated the explanation *and* left something unexplained! But using his renaming scheme and claiming that abstract entities are not real but behave as if they are, he must explain *how* they do so. And that currently is unexplained! Notice that we have effectively just derived [Dr Johnsons Criteria](Dr%20Johnsons%20Criteria.md): we should regard complex entities as real, which if we did not regard them as real would complicate our explanations. ### We give up on explanation if we say abstractions are not real There is yet *another* issue with arguing that abstractions are not real: this position means we are effectively giving up on explanations. Many of our best explanations reference abstract entities. To say that these are not real means that we cannot refer to them in our explanations. [Rational Inquiry Requires Pursuing Good Explanations](Rational%20Inquiry%20Requires%20Pursuing%20Good%20Explanations.md), and our explanations would become meaningfully *worse* if we can't reference abstract entities. Thus, it is irrational to give up on abstractions. --- Date: 20241230 Links to: Tags: References: * []() [^1]: Note that some renaming schemes would be completely appropriate. For instance, referring to "physically real" and "abstractly real" would be acceptable, for it acknowledges that both entities are real, while also denoting that they are slightly different by nature.